The flight distance from Cincinnati, Ohio, to Chicago, Illinois, is approximately 300 mi. On a recent round-trip between these cities in my private plane, I encountered a steady 25 mph headwind on the way to Chicago, with a 25 mph tailwind on the return trip. If my total flying time came to exactly 5 hr, what was my flying time to Chicago? What was my flying time back to Cincinnati? (Hint: The flight time between the two cities must add up to 5 hr.)

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The flight distance from Cincinnati, Ohio, to Chicago, Illinois, is approximately 300 mi. On a recent round-trip between these cities in my private plane, I encountered a steady 25 mph headwind on the way to Chicago, with a 25 mph tailwind on the return trip. If my total flying time came to exactly 5 hr, what was my flying time to Chicago? What was my flying time back to Cincinnati? (Hint: The flight time between the two cities must add up to 5 hr.)

Mathematics
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well you need to know the speed of the plane. distance = rate*time Let x be speed of plane, t1the time it took to Chicago, t2 the time to return to Cinci t1 + t2 = 5 --> t1 = 5-t2 trip to Chicago: 300/t1 = x-25 --> x = 300/t1 +25 return trip: 300/t2 = x+25 --> x = 300/t2 -25 setting the 2 equations equal and substituting 300/(5-t2) +25 = 300/t2 -25 300/t2 - 300/(5-t2) = 50 **for simplicity, i will just use t instead of t2 from now on** [300(5-t) -300t]/t(5-t) = 50 1500-600t = 50t(5-t) 50t^2 -850t +1500 = 0 t^2 -17t +30 = 0 (t-15)(t-2) = 0 t = 2 or 15, t2 can't be 15 because the total time is 5 hours Therefore, t1 = 3 hrs t2 = 2 hrs x = 125 mph
thanks!

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